Sweating refers to cooking on a lower heat with a small amount of fat. Sweating occurs before "browning" of any kind. Usually you would sweat vegetables, particularly onions, so adding them to some hot olive oil with a little salt and cooking them where they start to get translucent, but not browning would be sweating.

Like Mels said, it's important that the veggies not brown. You can help by moving them around the pan (but not too vigorously, otherwise they'll start to break up, which you also don't want), keeping the heat low, and by using a pan with high sides (so not a saute pan).

Also adding salt is key to sweating since the salt helps to draw out the liquid that's inside whatever you're sweating. Keeping the lid covered is also important since the liquid that comes out will evaporate more slowly.